A reversible heat engine converts one-fifth of the heat that it absorbs from the source into work. find the efficiency of the engine.

CONCEPT:

• The efficiency of a heat engine is defined as the ratio of the net work done by the engine in one cycle to the amount of heat absorbed by the working substance from the source.

The efficiency of a heat engine is given by:
( where Q2 is heat reject and Q1 is the heat absorbed )

CALCULATION:

Given W = 

• The first law of thermodynamics state that- The quantity of heat absorbed by the system will be equal to the sum of the increase in its internal energy and the external work done by the system on the surrounding.

 ,( ΔQ is the heat supplied to the system by the surrounding, ΔW is the work done by the system on the surroundings,  ΔU is the change in internal energy)

Q1 - Q2 = W ..........................(i) as internal energy (Δ U = 0) 

Q₂ = Q₁ - W = Q₁ - = 4/5Q₁ 

Q2 = 4/5Q1 

Hence,         ......(ii)

As we know the efficiency of a heat engine, on putting the value from (ii) we get 

=